© A. Panahi et al. 2022

1 Introduction

The Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015) is systematically scanning the sky in search of transiting exoplanets, producing hundreds of thousands of photometric light curves. TESS collects its data using four wide-field cameras with a relatively wide point spread function (PSF), namely on the order of 1 arcmin for bright stars (Sullivan et al. 2015). Faint unknown background eclipsing binary stars (BEBs) residing within the PSF of the TESS target star might therefore cause photometric modulations that would appear as planetary transits (e.g., Brown 2003; Cameron 2012). For this reason, photometric follow-up observations with high spatial resolution are required for the TESS objects of interest (TOIs) and their nearby stars to determine the actual source of the transit-like signal (e.g., Astudillo-Defru et al. 2020; Waalkes et al. 2021; Gan et al. 2021). This is usually done by ground-based seeing-limited photometric observations that can be used to differentiate between true and false-positive detections (e.g., Deeg et al. 2009; Collins et al. 2018; Lendl et al. 2020).

To identify the source of the modulations seen by TESS, one can also use the Gaia photometric data that have been accumulating since the launch of the European space mission in 2013 (Gaia Collaboration 2016). Although the main objective of the Gaia mission is high-accuracy astrometry of more than a billion objects (Gaia Collaboration 2021), Gaia also produces photometric measurements in its wide G band, which mostly covers the visible wavelength range (Jordi et al. 2010).

By itself, Gaia photometry is not optimized for detecting transiting planets, as the satellite scans the sky in an irregular low-cadence fashion, with typically a dozen observations per year (Gaia Collaboration 2016). On the other hand, TESS (during its prime mission) has been continuously monitoring the sky for about 27.5 days per sector, with a high cadence of 2 min for bright stars and 30 min for faint ones (Ricker et al. 2015). Nevertheless, thanks to the large number of stars sampled by Gaia and the photometric precision that can be on the order of a few millimagnitudes (mmag) or less (Gaia Collaboration 2021), two new transiting hot-Jupiters have already been discovered using Gaia photometry and validated via radial velocities (Panahi et al. 2022). More candidates were published in Gaia DR3 (Eyer et al. 2022).

The high angular resolution of Gaia currently enables it to safely resolve sources with a separation above ~0.7 arcsec, and it is expected to even improve in future data releases (Fabricius et al. 2021). In the case where a BEB is the origin of an apparent transit detected by TESS, Gaia may have already observed the eclipse photometrically. In this case, as Gaia is observing the undiluted and deeper transit, it can identify this star as the culprit of the TESS false positive. However, this is only possible if Gaia photometry has indeed sampled the eclipse events of the background binary. Short-period binaries might also display an ellipsoidal variability (e.g., Morris & Naftilan 1993; Faigler & Mazeh 2011) that can be detected by Gaia if the companion is sufficiently massive. If the secondary is sufficiently luminous, we might also see a secondary eclipse. On the other hand, the object eclipsing the background star might actually be a planet, shifting the planet-host candidacy to the nearby star. In case where the observed transit is due to the brightest star within the PSF, and the transit is deep enough to be discerned in the Gaia photometry, we can confirm the authenticity of the TOI as a transiting planet candidate (“on-target confirmation”).

Assessing the source of the transit signal has a time-sensitive nature, as successful identifications can save valuable observational resources. Joining the forces of the two space missions became imperative. We therefore initiated a collaboration between Gaia Data Processing and Analysis Consortium (DPAC; Gaia Collaboration 2016) and SubGroup 1 of the TESS Follow-up Observing Program Working Group (SG1; Collins 2019), liaised by the Tel Aviv University (TAU) group (which is part of DPAC), whose goal is to examine the TESS candidates with the help of the accumulating Gaia data. The TAU group examines the unpublished Gaia photometry to identify genuine and false candidates and shares those identifications with SG1 shortly after the release of the candidates. This collaboration started in February 2021, around the time TESS announced TOI-2400. The detection capability of the search gradually improved until June 2021, when TESS released TOI-3504.

This paper presents the details of the Gaia-TESS collaboration. We present the search methodology and list 124 BEBs, 124 on-target confirmations, and two planets in wide binary systems. Section 2 describes the search method for cases in which Gaia had measured dimming events in the TOIs or their neighboring stars and the initial assessment of whether these cases were on target. Section 3 presents the current results of the collaboration, including examples of on-target confirmations and identified BEBs. Section 4 presents an early assessment of the performance of the procedure and Sect. 5 discusses the significance of this collaboration and its future.

2 Search procedure

For each TOI, the procedure starts by retrieving the Gaia G-band photometry of each source within 1 arcmin of the position reported for the TOI; such sources are referred to as PSF neighbors hereafter. This radius was chosen in order to roughly accommodate the angular size of 3 TESS pixels, or an aperture area of π • 3² ≈ 30 pixels, which should include most of the accumulated light (see discussion below and Fig. 13 in Sullivan et al. 2015). In each light curve, we remove points that are brighter than the median magnitude by more than three times the median absolute deviation (MAD) of the photometric time series. After removing these points, only sources that have a minimum number of Gaia measurements are considered. Our most limiting criterion is the minimum number of in-transit points. We chose this number to be two, because one point is insufficient to constrain the periodicity and three would be too strict considering the sparsity of the Gaia photometry. We chose the minimum total number of points to be 14, somewhat arbitrarily, in an attempt to avoid dealing with small number statistics for the out-of-transit points.

Next, we explore the parameter space allowed by the uncertainties of the TESS parameters by applying a modified version of the box-fitting least square algorithm (BLS; Kovács et al. 2002) to the Gaia data, scanning a small region in the two-dimensional space around the TOI nominal period (P_TOI) and transit duration (d_ΤΟΙ), as reported by the TOI alert. The goal is to find the parameter values that produce the highest BLS signal residue (SR)¹ statistic (Kovács et al. 2002), while having at least two measurements in-transit. The search is restricted to a range of ±3Δ of the period and duration, where Δ is the respective uncertainty as reported by TESS.

We do not restrict the mid-transit time Τ at this stage and scan the whole range of phases in steps of one-tenth of the nominal transit duration. To incorporate the prior knowledge of the transit events, we apply Gaussian priors for the transit period, mid-transit time, and duration, resulting in a modified signal residue (MSR), $$MSR=SR-{\left(\right(\frac{P-P_{\text{TOI}}}{\Delta P_{\text{TOI}}}\left)\right)}^2-{\left(\right(\frac{T-T_{\text{TOI}}}{\Delta T_{\text{extended}}}\left)\right)}^2-{\left(\right(\frac{d-d_{\text{TOI}}}{\Delta d_{\text{TOI}}}\left)\right)}^2.$$(1)

The prior for T includes an extended uncertainty – taking into account the reported uncertainty for T_TOI and the accumulated uncertainty of the period – due to the number of cycles between the Gaia and TESS measurements: $$\Delta T_{\text{extended}}=\sqrt{{\left(\right(\Delta T_{\text{TOI}}\left)\right)}^2+{\left(\right(\frac{{\tilde{t}}_{\text{TESS}}-{\tilde{t}}_{Gaia}}{P_{\text{TOI}}}\Delta P_{\text{TOI}}\left)\right)}^2},$$(2)

where $\tilde{t}$ is the average observation time of the candidate, for each of the two space missions. Using the extended uncertainty for T lowers the weight of the mid-transit time prior, thus allowing the phase to shift and appear as a variation in the transit time.

The algorithm then selects the light curve that yields the highest MSR, using the best-fitting parameters to derive the transit depth δ, as seen by Gaia, and a merit function defined as the transit signal-to-noise ratio: $$S/N_{\text{T}}=\frac{\delta }{{\sigma }_{\text{OOT}}}\sqrt{N_{\text{IT}}}.$$(3)

Here σ_ΟΟΤ is the standard deviation of the out-of-transit (OOT) measurements (as a proxy to the inherent variability of the light curve, ignoring the transits) and N_IT is the number of in-transit (IT) Gaia measurements. We found most stars with S/N_t > 7 to be good candidates either for confirming or refuting the TOI candidacy and only very few with S/N_t < 7.

We proceed to inspect the candidates individually and group them into on-target and BEB candidates based on their angular distance from the TOI location. For on-target candidates, we make sure that the star is the brightest or one of the brightest stars in the TESS PSF, and that the transit depths of Gaia and TESS are similar. For BEB candidates, we check that the observed depth in the Gaia light curve is compatible with the depth reported by TESS, after correcting for dilution, and make sure the Gaia light curve of the target star shows no significant variability. We then proceed to visually examine the candidates to finally identify the BEB and on-target cases.

3 Results

3.1 Overview

The collaboration has so far gone through two phases. In the first preliminary phase (henceforth Phase I), during February-May 2021, the search procedure was still evolving, while producing partial results: 52 BEBs, 29 on-target confirmations, and one planet in a wide binary system. Since the second phase (Phase II) started in June 2021, a regular search has been performed. After examining 1600 TOIs in Phase II (3504–5103), the search yielded 72 BEBs, 95 on-target confirmations, and one planet in a binary system. As mentioned in Sect. 2, we included in our analysis only Gaia light curves with a minimum number of 14 measurements, after removing outliers.

We list the results of the two phases in Tables A.1–A.4. The tables include the period and depth of the released TOIs, the number of measurements in the Gaia light curve, N, the number of in-transit measurements, N_IT, and the derived depth of the Gaia transit (or eclipse in case of a BEB). All transit depths are given in parts per thousand (ppt). The depths in the Gaia photometry are calculated based on the box-shaped model of the BLS algorithm. The small number of points and the precision available do not allow us to fit a more accurate shape to the transit, which includes the limb-darkening effect (e.g., Mandel & Agol 2002; Hippke & Heller 2019).

In total, since February 2021, the search has yielded 124 BEBs, 124 on-target confirmations, and two planets in wide binary systems. We were also able to confirm a few dozen cases of known planets, but for conciseness we chose to exclude them from the present discussion.

3.2 Examples

We present the details of five specific cases that demonstrate the various types of discoveries made by the collaboration: two on-target cases confirmed by Gaia, for which the transits reported by TESS originate from the TOI target stars themselves, two BEBs, and one on-target transit in a wide binary system.

We obtained the TESS full-frame-image (FFI) photometry using the Python libraries Lightkurve (Lightkurve Collaboration 2018), Eleanor (Feinstein et al. 2019), and TESScut.MAST (Brasseur et al. 2019). We used the flatten( ) method of the Lightkurve library to detrend the data. In the following figures, the Gaia and TESS light curves are phase-folded with the period and mid-transit time obtained by our analysis.

3.2.1 On-target confirmations

Figures 1 and 2 show two on-target confirmations, with little or no dilution in the TESS light curves. We note that even two or three Gaia measurements in transit can be sufficient to confirm the transit events.

Fig. 1 On-target confirmation of TOI-4034. Top: Gaia and TESS light curves of TOI-4034, phase folded with a period of P = 1.80209590 days. Middle: zoomed-in view of the transit. Bottom: unfolded Gaia light curve. The Gaia light curves are marked by red circles, the TESS light curves are marked by light-gray squares, and the bins by blue squares. The duration of the transit, as reported by TESS, is marked by two vertical green dashed lines.

Fig. 2 On-target confirmation of TOI-4293. Top: Gaia and TESS light curves of TOI-4293, phase folded with a period of P = 1.62421090 days. Middle: zoomed-in view of the transit. Bottom: unfolded Gaia light curve. See Fig. 1 for details of the lines and symbols.

Fig. 3 BEB found near TOI-4216. Top: TESS light curve of TOI-4216, phase folded with a period of P = 2.18168090 days, together with the Gaia light curve of its BEB PSF neighbor. We note the clear ellipsoidal effect often seen in close-by binaries (see text). Bottom: unfolded Gaia light curve. See Fig. 1 for details of the lines and symbols.

3.2.2 Background eclipsing binaries

Figures 3 and 4 show two BEBs identified by Gaia photometry, both found less than 1 arcmin away from the position reported for their TOI. In both cases, the periodicity of the BEB star is consistent with the parameters of the TESS transit. The Gaia depths are larger, because the angular resolution of Gaia enables it to see the undiluted eclipse. The Gaia light curve of the TESS target star showed no significant variability. Figure 3 displays an ellipsoidal modulation, and Fig. 4 shows a secondary eclipse, both features point to the stellar nature of the companion.

3.2.3 Planet in a binary system

Figure 5 shows the transit of TOI-3722, suggesting an on-target identification. However, the significantly deeper transit observed by Gaia indicates a nearby star unresolved by TESS. Indeed, Gaia EDR3 lists two stars separated by ~1.2 arcsec at the TOI location: 490902499803340800 (A), exhibiting the transit in Gaia data, and 490902465447630976 (B) which does not exhibit any transit-like features. Based on the proximity between their locations on the sky, their parallax, and proper motion (Table 1), we propose that the two stars, with a projected separation of 830 ± 10 AU, form a wide binary. Using the criteria listed by El-Badry et al. (2021), the spatial parameters of the two stars are consistent with a bound binary system, although El-Badry et al. (2021) do not include the pair in their final catalog.

Fig. 4 BEB found near TOI-4346. Top: TESS light curve of TOI-4346, phase folded with a period of P = 3.907574060 days, together with the Gaia light curve of its BEB PSF neighbor. We note the clear secondary eclipse of the BEB centered at phase 0.5, indicating a circular orbit. The TESS light curve does not show the transit due to the vertical scale, determined by the deep eclipse. Bottom: unfolded Gaia light curve. See Fig. 1 for details of the lines and symbols.

Fig. 5 On-target confirmation of a planet in a binary system, TOI-3722. Top: Gaia and TESS light curves of TOI-3722, phase folded with a period of P = 1.078945850 days. The transit in the TESS light curve is diluted by the light of a neighboring star, which is suspected to form a binary system with the host star. Bottom: unfolded Gaia light curve. See Fig. 1 for details of the lines and symbols.

Fig. 6 Phase II: number of Gaia measurements per star for all 89 460 objects around the 1600 TOIs in Phase II. We note the cluster of stars with more than 200 measurements, which is due to the scanning law of Gaia at the beginning of the mission (see text).

4 Performance

4.1 Discovery rate

As explained above, we consider on-target confirmations or BEB detections only if there are at least two points in transit. Therefore, when estimating the expected rate of confirmations or detections, it is important to consider how many Gaia measurements per star were available at the time of the search. We chose to use the sample of 1600 Phase II TESS candidates (TOIs 3504–5103) for this purpose. In the Gaia database, we find 89 460 PSF neighbors of the 1600 TOIs, 77 049 of them having at least 14 Gaia measurements, which is the lower limit we chose for our current analysis (Fig. 6). There are about 200 measurements for one cluster of sources, which is due to stars in the ecliptic poles, which Gaia sampled extensively during the first 28 days of its operation (Gaia Collaboration 2016).

For a given star, the expected number of in-transit measurements, N_IT, can be estimated by multiplying the number of its Gaia measurements, N, by the fractional duration of the transit (duration divided by the period): $$N_{\text{IT}}=N\frac{d_{\text{TOI}}}{P_{\text{TOI}}}.$$(4)

When considering the discovery rate of on-target confirmations, it is important to note that the published transit depths of TOIs can be quite small. As the photometric precision of Gaia depends on the target brightness in a complicated manner (Riello et al. 2021), we consider only cases that are detectable by Gaia in terms of their expected S/N_T. We therefore only consider cases for which S/N_T > 5. This leaves 148 cases out of the 1600 from Phase II, of which only 85 had at least two measurements expected in transit².

BEBs on the other hand are expected to display substantially deeper eclipses, easily detectable by Gaia. However, the number of measurements of the star, N, for BEBs can only be estimated, because the identity of the eclipsing binary is not known in advance. We therefore use $\tilde{N}$ instead, which is the median number of Gaia measurements of the PSF neighbors of each TOI, and the corresponding expected number of measurements in transit, ${\tilde{N}}_{\text{IT}}$

Within the sample of 1600 TOIs in Phase II, there are 562 TOIs with ${\tilde{N}}_{\text{IT}}\ge 1.5$. According to Sullivan et al. (2015, their Fig. 2), the estimated fraction of BEB false positive TOIs is f_BEB = 0.15 ± 0.08, corresponding to 250 ± 125 BEBs in the Phase II sample and 87 ± 43 in the restricted sample of 562 TOIs.

For on-target detections, the fraction given by Sullivan et al. is f_on-target = 0.84 ± 0.12, corresponding to 1350 ± 190 in the Phase II sample and 73 ± 10 in the restricted sample of 85 TOIs. Comparing these estimates with the 72 detected BEBs (vs. 87 estimated) and 87 on-target confirmations with S/N_T > 5 (vs. 73 estimated), we suggest that the search for both BEBs and on-target confirmations is performing as expected, with a detection rate of ~5% for each case. The main limiting factor is the number of Gaia measurements.

Fig. 7 Phase II: distribution of the differences between the Gaia and TESS transit depths for the 95 on-target confirmations in Phase II. The mean and standard deviation of these differences are (μ, σ) = (1.3, 6.5) mmag.

4.2 Transit depths

Figure 7 presents a histogram of the differences between the transit depths as originally reported by TESS and the depths derived from the Gaia photometry, for the 95 on-target confirmations found in Phase II. The scatter is σ_d = 6.5 mmag, and therefore we adopt this value as the Gaia transit depth uncertainty for the on-target confirmations (Tables A.1 and A.3).

Figure 8 presents the dependence of the ratio between the Gaia and TESS depths on the angular distances between the identified Gaia sources and the corresponding TOI target stars. Naturally, the depth seen by Gaia is substantially larger for BEBs. As expected, the angular distance is small for on-target confirmations and large for BEBs, further delineating the separation between the two sets. Three out of the four BEB cases that had the smallest depth ratios were marked by the SG1 team as potential nearby planetary candidates (TOI-4211, TOI-4236 and TOI-4292). The BEB with the smallest depth ratio (TOI-3580) remained a BEB, as the stellar radius of the nearby host star is large enough to suggest a stellar eclipsing companion.

5 Discussion

This is an interim report on a collaborative effort of the TESS and Gaia teams to identify TOIs whose observed transit-like modulations are caused by faint neighboring BEBs and to confirm the TOI candidacy in some cases. The collaboration uses the growing database of Gaia epoch photometry and takes advantage of its high angular resolution and photometric precision, and has so far been able to confirm ~5% of the TESS candidates as on-target and dismiss another ~5% as BEBs.

As the BEB modulations are large and their eclipses are deep, the eclipses are easily seen in the Gaia photometry, as demonstrated by Figs. 3 and 4. In a few cases where the eclipse was found to occur in a neighboring star, the depth of the undiluted eclipse seen in the Gaia data was shallow enough to still be caused by a planet orbiting the nearby star. In these cases the candidacy was shifted from the target star of the TOI.

The main limiting factor for identifying BEBs is the number of Gaia photometric measurements during transits, which was too small for most BEBs to allow a safe identification. In the sample of 1600 TOIs, one could expect to have about 250 BEBs, while the search identified only 72, simply because of the small number of Gaia photometric measurements.

Figure 9 displays the angular distances of the detected BEBs in Phase II. One can see that most of them were found within 40 arcsec of their TOIs. Only 5 out of 72 BEBs are found in the range of 40–60 arcsec, indicating that the contamination drops substantially beyond 40 arcsec, equivalent to an area of approximately ten TESS pixels. We note that this is probably in accordance with (Sullivan et al. 2015, see their Fig. 14), who suggested an optimal collecting area of about ten pixels for a star of 10 mag. Furthermore, SG1 members privately reported that no BEBs further than 1 arcmin have been found so far, probably because these cases were mostly rejected early on by the TESS team via the centroid analysis method. However, the 60 arcsec radius might be too restrictive for a thorough search, and we will slightly enlarge this radius in the next Gaia-TESS phase.

Figure 10 shows the distribution of orbital periods for our detections of on-target confirmations and BEBs relative to all TOIs in Phase II, up to a period of 30 days. Given the sparsity of the Gaia photometry, we expected to mostly detect cases with short orbital periods, as the fractional duration of a transit (duty cycle) declines with larger periods as d/P ∝ P^−2/3 (Sackett 1999).

The Gaia data available to the collaboration consist of the first 34 months of operation. In the near future, the available photometry is expected to contain 66 months of data, greatly increasing the capability and discovery rate of the present method, and possibly even allowing us to refine the ephemerides of some candidates. When more Gaia measurements are available, we will be able to exclude more BEB alternatives. This will serve as a new way of confirming the on-target candidacy, allowing us to rule out all possible BEBs in neighboring stars and thus confirm the candidacy simply by elimination.

In the future, we plan to use the unpublished Gaia photometry, combined with the TESS photometry, to refine the TESS ephemerides, and to extend the BLS method to look for signs of transit-timing variations (TTV).

PLATO, the next transiting planet detection space mission, is expected to have a PSF of similar size to that of TESS (Rauer et al. 2016). By the time PLATO is operational, Gaia photometry will have already become public, allowing the community to perform similar checks that will allow quick identification of genuine transit candidates and save valuable resources required for ground-based follow-up observations.

Fig. 8 Phase II: transit depth ratios versus angular distance between the TOI targets and the Gaia detections, either BEBs or on-target confirmations. We omitted the transit-depth uncertainties for the on-target confirmations. For most of the BEBs, the uncertainties are smaller than the square sizes.

Fig. 9 Phase II: angular distances of BEBs from their TOIs.

Fig. 10 Phase II: normalized distribution of orbital periods for all TOIs up to a period of 30 days (gray) and detected on-target confirmations (lined green) and BEBs (dotted red).

Acknowledgements

We deeply thank the referee, Alexandre Santerne, for reviewing this paper and for the enlightening and helpful comments that greatly helped us improve the manuscript. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, some of which participate in the Gaia Multilateral Agreement. T.M. acknowledges support of the United States-Israel Binational Science Foundation (BSF), grant No. 2016069. S.Z. acknowledges support by the Ministry of Science and Technology, Israel (grant 3-18143), and a grant from the Tel Aviv University Center for AI and Data Science (TAD). We have used the following Python code libraries: Matplotlib (Hunter 2007), NumPy (Harris et al. 2020), AstroPy (Astropy Collaboration 2013), Lightkurve (Lightkurve Collaboration 2018), TESScut.MAST (Brasseur et al. 2019), Eleanor (Feinstein et al. 2019) and Pandas (Reback et al. 2021).

Appendix A Analysis results for Phase I and Phase II

References

All Tables

All Figures

Fig. 1 On-target confirmation of TOI-4034. Top: Gaia and TESS light curves of TOI-4034, phase folded with a period of P = 1.80209590 days. Middle: zoomed-in view of the transit. Bottom: unfolded Gaia light curve. The Gaia light curves are marked by red circles, the TESS light curves are marked by light-gray squares, and the bins by blue squares. The duration of the transit, as reported by TESS, is marked by two vertical green dashed lines.

In the text

	Fig. 2 On-target confirmation of TOI-4293. Top: Gaia and TESS light curves of TOI-4293, phase folded with a period of P = 1.62421090 days. Middle: zoomed-in view of the transit. Bottom: unfolded Gaia light curve. See Fig. 1 for details of the lines and symbols.
In the text

	Fig. 3 BEB found near TOI-4216. Top: TESS light curve of TOI-4216, phase folded with a period of P = 2.18168090 days, together with the Gaia light curve of its BEB PSF neighbor. We note the clear ellipsoidal effect often seen in close-by binaries (see text). Bottom: unfolded Gaia light curve. See Fig. 1 for details of the lines and symbols.
In the text

Fig. 4 BEB found near TOI-4346. Top: TESS light curve of TOI-4346, phase folded with a period of P = 3.907574060 days, together with the Gaia light curve of its BEB PSF neighbor. We note the clear secondary eclipse of the BEB centered at phase 0.5, indicating a circular orbit. The TESS light curve does not show the transit due to the vertical scale, determined by the deep eclipse. Bottom: unfolded Gaia light curve. See Fig. 1 for details of the lines and symbols.

In the text

	Fig. 5 On-target confirmation of a planet in a binary system, TOI-3722. Top: Gaia and TESS light curves of TOI-3722, phase folded with a period of P = 1.078945850 days. The transit in the TESS light curve is diluted by the light of a neighboring star, which is suspected to form a binary system with the host star. Bottom: unfolded Gaia light curve. See Fig. 1 for details of the lines and symbols.
In the text

	Fig. 6 Phase II: number of Gaia measurements per star for all 89 460 objects around the 1600 TOIs in Phase II. We note the cluster of stars with more than 200 measurements, which is due to the scanning law of Gaia at the beginning of the mission (see text).
In the text

	Fig. 7 Phase II: distribution of the differences between the Gaia and TESS transit depths for the 95 on-target confirmations in Phase II. The mean and standard deviation of these differences are (μ, σ) = (1.3, 6.5) mmag.
In the text

	Fig. 8 Phase II: transit depth ratios versus angular distance between the TOI targets and the Gaia detections, either BEBs or on-target confirmations. We omitted the transit-depth uncertainties for the on-target confirmations. For most of the BEBs, the uncertainties are smaller than the square sizes.
In the text

	Fig. 9 Phase II: angular distances of BEBs from their TOIs.
In the text

	Fig. 10 Phase II: normalized distribution of orbital periods for all TOIs up to a period of 30 days (gray) and detected on-target confirmations (lined green) and BEBs (dotted red).
In the text